The detectable subspace for the Friedrichs model

Brown, Brian M. ORCID: https://orcid.org/0000-0002-2871-6591, Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046, Naboko, Sergey and Wood, Ian 2019. The detectable subspace for the Friedrichs model. Integral Equations and Operator Theory 91 , 49. 10.1007/s00020-019-2548-9

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Abstract

This paper discusses how much information on a Friedrichs model operator can be detected from `measurements on the boundary'. We use the framework of boundary triples to introduce the generalised Titchmarsh-Weyl M-function and the detectable subspaces which are associated with the part of the operator which is `accessible from boundary measurements'. The Friedrichs model, a finite rank perturbation of the operator of multiplication by the independent variable, is a toy model that is used frequently in the study of perturbation problems. We view the Friedrichs model as a key example for the development of the theory of detectable subspaces, because it is sufficiently simple to allow a precise description of the structure of the detectable subspace in many cases, while still exhibiting a variety of behaviours. The results also demonstrate an interesting interplay between modern complex analysis, such as the theory of Hankel operators, and operator theory.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Computer Science & Informatics
Additional Information:	This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Publisher:	Springer Verlag (Germany)
ISSN:	0378-620X
Funders:	Russian Foundation for Basic Research, Knut and Alice Wallenberg Foundation
Date of First Compliant Deposit:	30 September 2019
Date of Acceptance:	27 September 2019
Last Modified:	20 May 2023 03:47
URI:	https://orca.cardiff.ac.uk/id/eprint/125702

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